Analysis And Construction Of S-Boxes With Lower Transparency Order

Differential power analysis(DPA),as a powerful attack method in power analysis attacks,using statistical analysis of the leakage power consumption characteristics of cryptographic equipment in the encryption operation rather than the mathematical characteristics of the encryption algorithm to recover all or part of the correct keys.As a non-invasive type of attack method,it is a serious threat to the security of embedded encryption system based on block cipher algorithms.In the block ciphers,S-boxes form the major non-linear components,and hence the security of this cryptosystems depend on the cryptographic properties of the S-boxes to a great extent,such as balanceness,algebraic degree,nonlinearity and differential uniformity etc..In recent years,the concept of transparency order proposed by E.Prouff,as a safety criterion to quantify the ability of the S-boxes to resist differential power analysis attacks,has been widely concerned.In this thesis,based on the relevant mathematical models of the differential power analysis attack,and combined with some classical cryptography security indexes of the S-boxes,we have obtained the following results:(1)According to the improved criterion of transparency order,relationships between the lower bound value of transparency order and the Walsh spectral value of the coordinate functions of S-boxes has been deduced and then we associated it with the non-linearity,pointing out a contrary relation between them.(2)In theory,the smaller the index value of the transparency order of S-boxes,the stronger the ability of its resistance to DPA attacks,therefore,we derived the specific lower bound values that can be achieved by the transparency order index in different cases where m is odd and even if the coordinate functions of(n,m)-function is the special case of a class of affine function;(3)Since the better shielded against differential and linear cryptanalysis attacks an S-box is,the more vulnerable it is to DPA attacks,in this respect,methods are required to obtain better S-boxes with a suitable tradeoff of cryptographic properties to resist both classical cryptanalysis and side channel attacks.As for the 4×4 S-boxes which are widely used in the lightweight block cipher algorithms,the number of this permutations is(2~4)!theoretically.Unlike the existing research methods that are only from the perspective of algorithms,in this thesis,we have constructed two kinds of balanced 4×4 S-boxes with lower transparency order values via the Maiorana-McFarland type functions and Bracken-Leander functions respectively from the perspective of mathematics,and then analysis have been made of their non-linearity,differential uniformity and the linear probability bias etc..furthermore,we comparative analysis of the cryptography security criterion of the S-boxes used in the existing block cipher algorithms to screened out two kinds of S-boxes with better comprehensive cryptographic properties.